4.7 Profitability (CLV)

The ultimate goal of customer retention is to increase the profitability of companies. Reinartz, Thomas, and Kumar (2005) linked customer acquisition, relationship duration, and profitability using a probit two-stage lease squares model. In the simultaneous equation model, a probit model was used to capture the acquisition process and a Tobit model was used to estimate the relationship duration of acquired customers. In the profitability model, these authors included as explanatory variables the firm actions, customer actions, control variables, predicted acquisition probability, and predicted relationship duration. To account for the right-censoring, the authors used a standard right-censored Tobit model to estimate the profitability.

Besides stochastic methods, researchers have developed deterministic methods to capture the optimal retention spending to maximize profitability. Just as Blattberg and Deighton [16] determined the optimal level of acquisition spending, they asked managers similar questions about companies' past retention activities to draw the retention curve. The answers to these questions indicate the retention expenditure per prospect, $R, the retention rate obtained as a result of that expenditure, r, and the ceiling rate on the retention curve. The curve is assumed to be exponential and captured by the equation

(4.40)

where is a parameter controlling the shape of the exponential curve. To draw the other part of the graph of customer equity against the retention budget, the authors assumed the same margin in each year, $m. The value of the customer in any given year is then given by

(4.41)

The authors then sum up the contribution for each year of the customer's projected life, add the contribution of a first-year customer, discount to a present value, and so get the amount of customer equity for that customer. From the upper and lower parts of the graph, the authors can easily determine the optimal level of retention spending which maximizes customer equity. They further expressed customer equity generated from customer acquisition and retention efforts in the following form:

(4.42)

where .

4.7.1 Empirical Example: Profitability (CLV)

The ultimate question for firms that are interested in customer retention is related to how profitable a current customer is likely to be in the future. In this example we will not focus on how a customer's expected future profitability, or CLV, is predicted. Instead, we want to focus on the drivers of CLV. Thus, we provide a prediction of CLV for each of the customers in the sample. We then want to use that prediction to understand which of the variables in our database help to explain the future value of a customer. If the drivers effectively explain the future value of a customer, we should be able to use the results of the estimation in the prediction of CLV for any customer not in the current sample. At the end of this example we should be able to do the following:

The information we need for this model includes the following list of variables:

In this case we have a dependent variable CLV which represents the expected discounted future profits from each customer. The CLV variable is continuous and not bound by any threshold. Thus, given the assumption that CLV is normally distributed around a specific mean, we merely want to run an OLS regression to uncover the drivers of CLV. We get an equation in the following format:

where CLV is the customer lifetime value of a given customer, X is the matrix of independent variables, β is the vector of coefficients of the independent variables, and ε is the random error term which is normally distributed with a mean of 0 and variance of σ². We get the following results when we estimate the model:

We gain the following insights from these results. We find that all the variables with the exception of Purchase_Rate and Married are statistically significant at p < 0.05. We find that Avg_Order_Quantity is positive, suggesting that the higher the average past order values of the customer, the higher the CLV. We find that Avg_Crossbuy is positive, suggesting that the more a customer has bought across multiple categories in the past, the higher the customer's CLV. We find that Ret_Expense is positive with a diminishing return, as noted by the positive coefficient on Ret_Expense and the negative coefficient on Ret_Expense_SQ. This means that marketing efforts to retain and build relationships with the customer do cause the customer to have a higher CLV. Then after the threshold is reached, marketing efforts actually decrease the CLV on average. This is likely due to the fact that overly contacting customers can often strain the relationship between the customer and firm, and because when marketing efforts lose effectiveness the costs continue to increase without corresponding profit increases. We find that four of the customer characteristic variables are positive (Gender, Income, First_ Purchase, and Loyalty) suggesting that customers who are male, with a higher income, higher first purchase value, and members of the loyalty program are likely to have a higher CLV.

Our next step is to predict the value of CLV to see how well our model compares to the actual values. We do this by starting with the equation for expected CLV. Given that we have an OLS regression model, we obtain the following equation:

In this case X is the matrix of independent variable values from the CLV equation and β is the vector of parameter estimates from the CLV equation. Once we have predicted CLV for each of the customers we want to compare this to the actual value from the database. We do this by computing the MAD. The equation is as follows:

We find for the acquired customers that MAD = 39.01, or on average $39.01 from the actual CLV. If we were to instead use the mean value of CLV ($1126.73) across all customers as our prediction for all customers (this would be the benchmark model case), we would find that MAD = 734.51, or on average $734.51 from the actual CLV. As we can see, our model does a significantly better job of predicting the value of CLV than the benchmark case.

4.7.2 How Do You Implement it?

In this example we used PROC Reg from SAS to estimate the OLS regression model to explain the variance of CLV. While we did use SAS to implement this modeling framework, programs such as SPSS, MATLAB, R, and GAUSS can be used as well.